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arXiv · 2601.17766

Computing L-functions of $ \lambda $-adic representations of global function fields

David Kurniadi Angdinata
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Abstract

The L-function $ L(\rho_\lambda, s) $ of an almost everywhere unramified $ \lambda $-adic representation $ \rho_\lambda $ of a global function field $ \mathbb{F}_q(C) $ is known to be a rational function in $ q^{-s} $ satisfying a functional equation up to some complex sign $ \epsilon(\rho_\lambda) $. This paper presents a systematic framework to compute the coefficients of $ L(\rho_\lambda, s) $ and its sign $ \epsilon(\rho_\lambda) $ with some explicit examples.

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David Kurniadi Angdinata. 2026-01-25. Computing L-functions of $ \lambda $-adic representations of global function fields. https://arxiv.org/abs/2601.17766

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